SOLUTION: A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7

Question 1132192: A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

P(5) = 4/36 = 1/9
P(7) = 6/36 = 1/6
P(neither 5 nor 7) = 26/36 = 13/18

P(5 before 7) =
P((5 on first flip) OR
(neither 5 nor 7 on first flip AND 5 on second flip) OR
(neither 5 nor 7 on first flip AND neither 5 nor 7 on second flip AND 5 on third flip) OR
...) =

1/9 + (13/18)(1/9) + (13/18)(13/18)(1/9) + ...

This is an infinite geometric series with first term a = 1/9 and common ratio r = 13/18.

The formula for the sum of an infinite geometric series with first term a and common ratio r (|r|<1) is

You can do the calculation.
Answer by ikleyn(52811)   (Show Source): You can put this solution on YOUR website!
.
A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7
~~~~~~~~~~~~~~~~~~

            As I read the problem, I understand it in this way (literally as it is written) :

A pair of dice is rolled together. As soon as a sum of either 5 or 7 is obtained, the experiment stops. What is the probability that the last obtained sum is 5 ?

            It is different from reading by @greenestamps, who counts when and how the "7" will be obtained after getting of "5".

            In my interpretation, I do not concern what will happen after EITHER 5 OR 7 will be obtained - it is the command
            to stop the experiment.

            Therefore, my solution is different, although the answer is the same number.

Solution

P(5) = = <<<---=== of 6x6 = 36 sample cases only 4 produce the sum of 5. P(7) = = <<<---=== of 6x6 = 36 sample cases only 6 produce the sum of 7. The problem asks to find a conditional probability of getting the sum of 5 under the condition that this sum is EITHER "5" OR "7". Then this conditional probability is = = = = 0.4 = 40%. ANSWER

RELATED QUESTIONS
A pair of dice is rolled. What is the probability that the sum of the numbers rolled is... (answered by Alan3354,greenestamps)
Solve the problem and show the solutions 1. Pair of dice is rolled. What is the... (answered by ikleyn,Alan3354)
A pair of dice are rolled. What is the probability that the number rolled will be less... (answered by stanbon)
A pair of fair dice are rolled. What is the probability that both dice either turn up the (answered by ewatrrr)
Two dice are rolled. Find the probability of getting a sum of 5, 6, or... (answered by ikleyn)
Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both (answered by Big Poop)
Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both (answered by Big Poop)
Two dice are rolled. Find the probability of getting a 5 on either die or the sum of both (answered by Edwin McCravy)
A pair of 6-sided dice is rolled 10 times. What is the probability that in exactly 3 of... (answered by Boreal)